NEW YORK (AP) — In a significant victory amid a push for paid sick time laws around the country, city lawmakers voted Wednesday to make businesses provide the benefit to an estimated 1 million workers who don’t have it now.

Saying they hoped that requiring sick leave in the nation’s largest metropolis would set an example, City Council members positioned New York to become the most populous place to approve such a law during a campaign that has scored several victories but also a number of defeats. A mayoral veto is expected, but so is an override.

Advocates see the measure as a signal accomplishment, although it has some significant limits and conditions.

“It’s very important that it’s happening in the biggest city,” said Ellen Bravo, executive director of Family Values at Work, which promotes paid sick time initiatives around the country. Besides the big-city setting, the New York measure also attracted some boldface-name backers, including feminist Gloria Steinem and “Sex and the City” actress Cynthia Nixon.

Supporters see paid sick time as a basic matter of working conditions, akin to a minimum wage, and a way to stop coughing, sneezing employees from spreading germs to their colleagues and customers. The New York measure’s sponsor, Councilwoman Gale Brewer, says it’s about “a workplace that is safe, fair and respectful of the lives of workers.”

Critics say some small enterprises can’t afford the benefit and businesses resent the implication that they’re forcing ailing employees to come in to work and creating a public health problem.

Government should let bosses and employees work out sick time arrangements on their own, they say. Some restaurants, for example, have shift-switching systems instead of paid time off, partly on the premise that servers would rather not lose out on tips.

“These are sort of one-size-fits-all policies that don’t work well in many industries,” said Michael Saltsman of the Employment Policies Institute, a research group financed by foundations, businesses and individual donors.

Mayor Michael Bloomberg suggested some companies would lay off employees to stay below the New York measure’s threshold for paying for sick leave.

“To make it more uneconomical for companies to employ (people) is just not good business for the city,” Bloomberg said after an unrelated event Wednesday.

But advocates say it’s unlikely a business would forgo a needed worker to avoid the cost of a handful of sick days.

Employees of businesses with 20 or more workers would get up to five paid sick days a year beginning in April 2014; the benefit would kick in by October 2015 at enterprises with 15 to 19 workers. All others would have to provide five unpaid sick days per year, meaning that workers couldn’t get fired for using those days.

Manufacturing companies would be exempt because they’re struggling, Council Speaker Christine Quinn said.

She had declined for three years to bring the proposal to a vote, but she came under increasing pressure to support it this year, when she’s also campaigning for mayor. She says the measure evolved to strike a proper balance between workers’ needs and employers’ interests.

Workers could choose to work extra hours instead of taking sick time, a provision that could be attractive to those who would rather trade shifts than call in sick.

Some advocates said they would continue to push for having all the workers get paid leave, and some aren’t thrilled with a provision that could push the requirement off if the city’s economy majorly worsens.

“People get sick in all economic times,” Councilman Jumaane Williams said before casting his yes vote. The measure passed 45-3.

Supporters view the New York measure as a bellwether for a cause that’s now being pressed in Maryland, Oregon, Vermont and Washington state by various groups, including the Working Families Party. Saltsman, though, questions whether the idea will gain traction outside a liberal core of cities.

Paid sick time measures have been approved in Portland, Ore.; San Francisco; Seattle; Washington, D.C.; and the state of Connecticut.